The field of pulsar astronomy encompasses a rich breadth of astrophysical topics. The research in this thesis contributes to two particular subjects of pulsar astronomy: gravitational wave science, and identifying celestial sources of pulsed radio emission. We first investigated the detection of supermassive black hole (SMBH) binaries, which are the brightest expected source of gravitational waves for pulsar timing. We considered whether two electromagnetic SMBH tracers, velocity-resolved emission lines in active nuclei, and radio galactic nuclei with spatially-resolved, flat-spectrum cores, can reveal systems emitting gravitational waves in the pulsar timing band. We found that there are systems which may in principle be simultaneously detectable by both an electromagnetic signature and gravitational emission, however the probability of actually identifying such a system is low (they will represent much less than 1% of a randomly selected galactic nucleus sample). This study accents the fact that electromagnetic indicators may be used to explore binary populations down to the 'stalling radii' at which binary inspiral evolution may stall indefinitely at radii exceeding those which produce gravitational radiation in the pulsar timing band. We then performed a search for binary SMBH holes in archival Very Long Baseline Interferometry data for 3114 radio-luminous active galactic nuclei. One source was detected as a double nucleus. This result is interpreted in terms of post-merger timescales for SMBH centralisation, implications for 'stalling', and the relationship of radio activity in nuclei to mergers. Our analysis suggested that binary pair evolution of SMBHs (both of masses >108M circled bullet) spends less than 500Myr in progression from the merging of galactic stellar cores to within the purported stalling radius for SMBH pairs, giving no evidence for an excess of stalled binary systems at small separations. Circumstantial evidence showed that the relative state of radio emission between paired SMBHs is correlated within orbital separations of 2.5 kpc. We then searched for transient radio events in two archival pulsar surveys, and in the new High Time Resolution Universe (HTRU) Survey. We present the methodology employed for these searches, noting the novel addition of methods for single-event recognition, automatic interference mitigation, and data inspection. 27 new neutron stars were discovered. We discuss the relationship between “rotating radio transient” (RRAT) and pulsar populations, finding that the Galactic z-distribution of RRATs closely resembles the distribution of pulsars, and where measurable, RRAT pulse widths are similar to individual pulses from pulsars of similar period, implying a similar beaming fraction. We postulate that many RRATs may simply represent a tail of extreme-nulling pulsars that are “on” for less than a pulse period; this is supported by the fact that nulling pulsars and single-pulse discoveries exhibit a continuous distribution across null/activity timescales and nulling fractions. We found a drop-off in objects with emissivity cycles longer than 300 seconds at intermediate and low nulling fractions which is not readily explained by selection effects. The HTRU deep low-latitude survey (70-min. pointings at galactic latitudes |b| < 3.5 degrees and longitudes −80 degrees < l < 30 degrees) will be capable of exploring whether this deficit is natural or an effect of selection. The intriguing object PSR J0941–39 may represent an evolutionary link between nulling populations; discovered as an sparsely-pulsing RRAT, in follow-up observations it often appeared as a bright (10 mJy) pulsar with a low nulling fraction. It is therefore apparent that a neutron star can oscillate between nulling levels, much like mode-changing pulsars. Crucially, the RRAT and pulsar-mode emission sites are coincident, implying that the two emission mechanisms are linked. We estimate that the full HTRU survey will roughly quadruple the known deep-nulling pulsar population, allowing statistical studies to be made of extreme-nulling populations. HTRU's low-latitude survey will explore the neutron star population with null lengths lasting up to several hours. We lastly reported the discovery of 16 pulses, the bulk of which exhibit a frequency sweep with a shape and magnitude resembling the “Lorimer Burst” (Lorimer et al. 2007), which three years ago was reported as a solitary radio burst that was thought to be the first discovery of a rare, impulsive event of unknown extragalactic origin. However, the new events were of clearly terrestrial origin, with properties unlike any known sources of terrestrial broad-band radio emission. The new detections cast doubt on the extragalactic interpretation of the original burst, and call for further sophistication in radio-pulse survey techniques to identify the origin of the anomalous terrestrial signals and definitively distinguish future extragalactic pulse detections from local signals. The ambiguous origin of these seemingly dispersed, swept-frequency signals suggest that radio-pulse searches using multiple detectors will be the only experiments able to provide definitive information about the origin of new swept-frequency radio burst detections. Finally, we summarise our major findings and suggest future work which would expand on the work in this thesis.